Chapter 5 – Quadratic Functions and Factoring 5.5 – Factoring Using Special Patterns

5.5 – Factoring Using Special Patterns Today we will be learning: Factoring using special patterns

5.5 – Factoring Using Special Patterns Some quadratic expressions can be factored using special patterns. Example: (x + 5)(x – 5). Find the product using FOIL.

5.5 – Factoring Using Special Patterns Difference of Two Squares Pattern Algebra: a2 – b2 = (a + b)(a – b) Example: x2 – 4 = (x + 2)(x – 2)

5.5 – Factoring Using Special Patterns Example 1 Factor the expression. m2 – 64 p2 – 49 16n2 – 25

5.5 – Factoring Using Special Patterns To see another special pattern, find the product of (x + 3)2 using FOIL.

5.5 – Factoring Using Special Patterns Perfect Square Trinomial Patterns Algebra: a2 + 2ab + b2 = (a + b)2 Example: x2 + 14x + 49 = (x + 7)2 Algebra: a2 – 2ab + b2 = (a – b)2 Example: x2 – 10x + 25 = (x – 5)2

5.5 – Factoring Using Special Patterns Example 2 Factor the expression. m2 + 12m + 36 16p2 + 40p + 25 9n2 – 24n + 16

5.5 – Factoring Using Special Patterns Example 3 Factor 4m2 – 24m + 36

5.5 – Factoring Using Special Patterns Example 4 Solve 4r2 – 20r = -25

5.5 – Factoring Using Special Patterns Example 5 The time (in seconds) it takes a ball to hit the ground after dropping it from the top of a 64 foot building can be found using the function h = -16t2 + 64 where h is the height of the ball. Find the length of time it takes for the ball to reach the ground (h = 0).

5.5 – Factoring Using Special Patterns HOMEWORK 5.5 Worksheet Odd Numbers

5.5 – Factoring Using Special Patterns CLASSWORK/HOMEWORK 5.5 Worksheet Even Numbers